Question

mn is the midsegment of the trapezoid abcd. what is the length of segment ab?
a. 8
b. 9
c. 10
d. 14

Explanation:

Step1: Recall the trapezoid midsegment formula

The formula for the midsegment \(MN\) of a trapezoid \(ABCD\) (where \(MN=\frac{AB + CD}{2}\), \(MN\) is the mid - segment, \(AB\) and \(CD\) are the bases of the trapezoid).

Step2: Substitute the known values into the formula

We know that \(MN = 7\) and \(CD=6\). Substituting into \(MN=\frac{AB + CD}{2}\), we get \(7=\frac{AB + 6}{2}\).

Step3: Solve the equation for \(AB\)

Multiply both sides of the equation \(7=\frac{AB + 6}{2}\) by \(2\): \(2\times7=AB + 6\), which simplifies to \(14=AB + 6\). Then subtract \(6\) from both sides: \(AB=14 - 6\).

Answer:

\(AB = 8\), so the answer is A.